This KB document explains how to open up a shared mailbox on an iPad. This is the only way currently to open a shared mailbox on a iPad.
1. On a desktop, log into the user's email through OWA.
2. Go to "Open Another Mailbox..." and open the desired shared mailbox.
3. Copy the webpage URL of the shared mailboxes inbox. (e.g. https://firstname.lastname@example.org/)
4. Create a new email and paste the website URL into it and send it to the users main email.
5. Now on the iPad, log into the user's email through OWA.
6. Open the email that we just sent to the main email and click on the link. This should open the shared mailbox they would like opened.
7. Create an app of the webpage by pressing on the box with an arrow pointing up (should be next to the website URL), on the bottom row you should see Add to reading list, add bookmark, add to favorites, etc. Scroll over until you see the option "Add to Home Screen". This will create a link in the form of an app to access the shared mailbox whenever needed.